Chelsea are said to have made a £34million offer for the 20-year-old striker, who has drawn great attention in the Scottish Premiership.
While Express Sport understands Celtic value Dembele at £40m, Chelsea are apparently continuing their last-minute pursuit.
According to the Daily Mail, the Blues have not balked at the hefty fee it would take to land the Frenchman, and they are ready to test Celtic’s resolve.
If Chelsea sign Moussa Dembele from Celtic, it could see Michy Batshuayi leave for West Ham
If Chelsea match Celtic’s price-tag, they may have to reconsider their stance
Brendan Rodgers has insisted Celtic will not sell their star man this month, and the manager has already blocked Chelsea from taking goalkeeper Craig Gordon at the end of the window.
But Conte is lining up a massive offer as he steps up his interest in Dembele.
The hitman, who has 20 goals already this term, is happy to stay at the club until at least the summer.
But if Chelsea match Celtic’s price-tag, they may have to reconsider their stance on the player’s future.
Brendan Rodgers is intent on keeping Moussa Dembele at Celtic this month
Chelsea transfers: Deadline day ins and outs rumours rated
Mon, January 30, 2017
Football Whispers have rated Sunderland's chances in the transfer market ahead of deadline day (1 – unlikely, 5 – likely)
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Football Whispers have rated the likelihood of Chelsea transfer deals (out of 5)
And the Blues will hope to complete the signing of Dembele in plenty of time before today’s 11pm deadline so they have time for another switch.
The report adds £33m summer signing Batshuayi will be allowed to join West Ham on loan.
Slaven Bilic has ended interest in Brentford striker Scott Hogan, but the Hammers are still looking to sign a top frontman if available.
Chelsea pipped West Ham to Batshuayi at Marseille in August, and they have since enquired over taking the Belgium international to give him game time.
Michy Batshuayi scored for Chelsea in their 4-0 FA Cup win vs Brentford on Saturday in a rare start
The 23-year-old has been restricted to just substitute appearances in the Premier League this season, while a switch to the London Stadium could help him find his feet in English football.
Diego Costa has been preferred all season, having led Chelsea’s title charge, but Dembele is seen as a long-term replacement in case their star forward leaves Stamford Bridge in the summer for either China or Atletico Madrid.
Even though Celtic only paid Fulham £500,000 for Dembele at the start of the campaign, Chelsea are prepared to spend big with Conte’s transfer budget boosted by the £52m sale of Oscar earlier this month.